In this work, we use the spline model detailed above to model the population of spin magnitudes \(a\)  and tilt angles \(\cos \theta \) .
Consistent with [1]}, [2]}, we model these parameters as independent and identically distributed.
The total spin population model is
\(\pi _{\rm spin}(\eta |\Lambda _s) = p_{a}(a_1) p_{a}(a_2) p_{t}(\cos \theta _1) p_{t}(\cos \theta _2),\) 
